Honest universality
Nachum Dershowitz, Evgenia Falkovich · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2012
We extend the notion of universality of a function, due to Turing, to arbitrary (countable) effective domains, taking care to disallow any cheating on the part of the representations used. Then, we can be certain that effective universal functions cannot simulate non-effective functions.